Part of the complexity of fluid flow stems from the many aspects, or "dimensions," that characterize a particular flowfield. These dimensions must be fully understood in order to effectively analyze and comprehend the flow.
Every flowfield “lives” somewhere in the
four-dimensional domain depicted below.
Compressibility – the yellow dimension
The physical state of the fluid may be liquid, gas, or a 2-phase mixture of the two. Additional states are possible involving the solid phase and, at the extreme end of the gas phase, plasmas. While all fluids can exist in any of these states, particular flows may encounter a subset of this dimension.
The transonic flow with condensation past this F-4 aircraft illustrates combined gas and 2-phase flows. Arrow indicates shock wave - a discontinuity in the flowfield.
Thermochemistry – the red dimension
In reality, all fluids are capable of chemical reaction – such as the combustion of a fuel with an oxidizer. However, particular flows may not experience this complex phenomenon. This leads to opportunities for considerable simplification in analysis. Simple fluids have thermodynamic and transport properties which remain constant or experience limited types changes with changes in their environment. For example, tap water has essentially constant specific heat and viscosity for flows in this regime.
Luminous flowfield of hot, ionized combustion product gases
is observed in this combustion chamber test.
Viscosity – the blue dimension
This shlieren movie of an aeroacoustic Computational Fluid Dyanmics (CFD) solution shows unsteady turbulent flow with generated sound waves.
All fluids have finite viscosity, or intrinsic resistance to shearing. Many flowfields of practical interest may be approximated as inviscid, yet be analysed to obtain the desired data. An inviscid analysis, for example, may produce an accurate pressure load. Viscous flows range from laminar to turbulent. Laminar flows may be steady with time, and are characterized by coherent movement of fluid particles. Turbulent flows vary with time, and are characterized by random, chaotic motion of the fluid particles. This often occurs on a microscopic scale imposed on a coherent macroscopic flow. A classic demonstration is a the flow from a water faucet. At small flow rates the flow is laminar, and nearly transparent. As the flow rate is increased a “transition” to turbulence occurs. The stream is now opaque and the turbulent motion of the flow can be readily observed. In nature, and in engineering applications, the vast majority of flowfields are indeed turbulent.
Time – the gray dimension
Fluid flows may be steady or vary with time. The flow of gas through an automobile engine is unsteady due to the reciprocating motion of the pistons. All turbulent flows are, by definition, unsteady. Many turbulent phenomena however, may be well modeled with time-average approximations. This produces substantial economy in the computation, and most turbulent flow analyses are conducted in this manner.
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